




錯視の科学館 展示 No. 14 


数式傾斜錯視 








Tilt Illusions of Mathematical
formulae


















新井仁之 (Hitoshi Arai) 











Hitoshi Arai (Univ. Tokyo, Japan) discovered the following tilt illusion
which consists of mathematical formulae (November 15, 2009). 

















© Hitoshi Arai 2009 












These are in the draft of my book entitled ''Wavelets'' (Kyoritsu Publ.
Tokyo, 2010). 


Mathematical meaning : The above formulae represent a construction of wavelet
vectors from a scaling filter and a wavelet filter. 













Nov. 18, 2009. 






I informed Professor Akiyoshi Kitaoka the tilt illusion of math. formulae,
and immediately I received his message ''I would like to see the clockwise
version''. I sought it in my draft, and found out a mathematical formula
which seems to tilt clockwise. The following illusion is a modified version
of the original one, but the mathematical meaning is equivalent. 



















©Hitoshi Arai 2009 












Mathematical meaning: This is the set of decomposition coefficients of
the signal x by the scaling vectors and wavelet vectors. 




The above mentioned formulae were made by LaTeX 2e. 













Sicence Museum of Visual Illusions 











Entrance 




















